Complete the following:
Q: Hurricane Katrina hit New Orleans on August 29, 2005. The National Weather Service Forecast Office maintains online archives of climate data for all U.S. cities and areas. These archives allow us to find out, for example, how the rainfall in New Orleans that August compared to the other months of 2005. The table below shows the National Weather Service data (rainfall in inches) for New Orleans in 2005.
January 4.41
February 8.24
March 4.69
April 3.31
May 4.07
June 2.52
July 10.65
August 3.77
September 4.07
October 0.04
November 0.75
December 3.32
a. Calculate the z score for August. (Note: These are raw data for the population, rather than summaries, so you have to calculate the mean and the standard deviation first.)
b. What is the percentile for the rainfall in August? Does this surprise you? Explain.
c. When our results surprise us, it is worthwhile to examine the individual data more closely, or even to go beyond the data we have. The daily climate data, as listed by this source, for August 2005 show the code "M" next to August 29, 30, and 31 for all climate statistics. The code indicates that "[REMARKS] ALL DATA MISSING AUGUST 29, 30, AND 31DUE TO HURRICANE KATRINA." Pretend it was your consulting job to determine the percentile for that August. Write a brief paragraph for your report, explaining why the data you generated are likely to be inaccurate.
d. What raw scores would mark the cutoff for the top and bottom 10% for these data? Based on these scores, what months had extreme data for 2005? Why should we not trust these data?